Q. The temperature of the hydrogen at which the average speed of its molecules is equal to that of oxygen molecules at a temperature of $31℃,$ is
A) $- 216℃$
B) $- 235℃$
C) $- 254℃$
D) $- 264℃$
Explanation
(c) $v_{av} = \sqrt{\frac{8RT}{\pi M}} \Rightarrow T \propto M\ \ \ \lbrack\because v_{av},\ R \rightarrow constant\rbrack$
$\Rightarrow \frac{T_{H_{2}}}{T_{O_{2}}} = \frac{M_{H_{2}}}{M_{O_{2}}} \Rightarrow \frac{T_{H_{2}}}{(273 + 31)} = \frac{2}{32}$
$\Rightarrow T_{H_{2}} = 19\ K = - 254℃$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.